To find the expression equivalent to [tex]\(\sqrt{27} - \sqrt{12} + \sqrt{48}\)[/tex], we'll first simplify the square roots:
1. Simplifying [tex]\(\sqrt{27}\)[/tex]:
[tex]\[
\sqrt{27} = \sqrt{9 \cdot 3} = \sqrt{9} \cdot \sqrt{3} = 3\sqrt{3}
\][/tex]
2. Simplifying [tex]\(\sqrt{12}\)[/tex]:
[tex]\[
\sqrt{12} = \sqrt{4 \cdot 3} = \sqrt{4} \cdot \sqrt{3} = 2\sqrt{3}
\][/tex]
3. Simplifying [tex]\(\sqrt{48}\)[/tex]:
[tex]\[
\sqrt{48} = \sqrt{16 \cdot 3} = \sqrt{16} \cdot \sqrt{3} = 4\sqrt{3}
\][/tex]
After simplifying the square roots, we substitute them back into the original expression:
[tex]\[
3\sqrt{3} - 2\sqrt{3} + 4\sqrt{3}
\][/tex]
Now, we combine like terms by adding and subtracting the coefficients of [tex]\(\sqrt{3}\)[/tex]:
[tex]\[
(3 - 2 + 4) \sqrt{3} = 5 \sqrt{3}
\][/tex]
Therefore, the choice equivalent to the expression [tex]\(\sqrt{27} - \sqrt{12} + \sqrt{48}\)[/tex] is:
[tex]\[
\boxed{5 \sqrt{3}}
\][/tex]
